基于MATLAB的PUMA560机器人运动仿真与轨迹规划5.docx

基于MATLAB的PUMA560机器人运动仿真与轨迹规划5.docx

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基于MATLAB的PUMA560机器人运动仿真与轨迹规划5

Themovementsimulationandtrajectoryplanningof

PUMA560robot

Shibozhao

Abstract:

Inthisessay,weadoptmodelingmethodtostudyPUMA560robotintheuseofRoboticsToolboxbasedonMATLAB.Wemainlyfocusonthreeproblemsinclude:

theforwardkinematics,inversekinematicsandtrajectoryplanning.Atthesametime,wesimulateeachproblemabove,observethemovementofeachjointandexplainthereasonfortheselectionofsomeparameters.Finally,weverifythefeasibilityofthemodelingmethod.

Keywords:

PUMA560robot;kinematics;RoboticsToolbox;Thesimulation;

.Introduction

Asautomationbecomesmoreprevalentinpeople’slife,robotbeginsmorefurthertochangepeople’sworld.Therefore,weareobligedtostudythemechanismofrobot.Howtomove,howtodeterminethepositionoftargetandtherobotitself,andhowtodeterminetheanglesofeachpointneededtoobtaintheposition.Inordertostudyrobotmorevalidly,weadoptrobotsimulationandobject-orientedmethodtosimulatetherobotkinematiccharacteristics.Wehelpresearchersunderstandtheconfigurationandlimitoftherobot’sworkingspaceandrevealthemechanismofreasonablemovementandcontrolalgorithm.Wecanlettheusertoseetheeffectofthedesign,andtimelyfindouttheshortcomingsandtheinsufficiency,whichhelpusavoidtheaccidentandunnecessarylossesonoperatingentity.ThispaperestablishesamodelforRobotPUMA560byusingRoboticsToolbox,andstudytheforwardkinematicsandinversekinematicsoftherobotandtrajectoryplanningproblem.

.TheintroductionoftheparametersforthePUMA560robot

PUMA560robotisproducedbyUnimationCompanyandisdefinedas6degreesoffreedomrobot.Itconsists6degreesoffreedomrotaryjoints（Thestructurediagramisshowninfigure1）.Referringtothehumanbodystructure,thefirstjoint（J1）calledwaistjoints.Thesecondjoint（J2）calledshoulderjoint.Thethirdjoint（J3）calledelbowjoints.ThejointsJ4J5,J6,arecalledwristjoints.Where,thefirstthreejointsdeterminethepositionofwristreferencepoint.Thelatterthreejointsdeterminetheorientationofthewrist.TheaxisofthejointJ1locatedverticaldirection.TheaxisdirectionofjointJ2,J3ishorizontalandparallel,a3metersapart.JointJ1,J2axisareverticalintersectionandjointJ3,J4axisareverticalcrisscross,distanceofa4.Thelatterthreejoints’axeshaveanintersectionpointwhichisalsooriginpointfor{4},{5},{6}coordinate.（Eachlinkcoordinatesystemisshowninfigure2）

Fig1

thestructureofpuma560

Fig2

thelinkscoordinateofpuma560

WhenPUMA560Robotisintheinitialstate,thecorrespondinglinkparametersareshowedintable1.

Theexpressionofparameters:

Letlengthofthebar

representthedistancebetween

and

along

.

Torsionangle

denotetheanglerevolving

from

to

.

Themeasuringdistancebetween

and

along

is

.

Jointangle

istheanglerevolvingfrom

to

along

.

Table1

theparametersofpuma560

link

Range

1

0

0

90

0

-160~160

2

-90

0

0

0.1491

-225~45

3

0

0.4318

-90

0

-45~225

4

-90

-0.0213

0

0.4331

-110~170

5

90

0

0

0

-100~100

6

-90

0

0

0

-266~266

.ThemovementanalysisofPuma560robot

3.1Forwardkinematic

Definition:

Forwardkinematicsproblemistosolvetheposeofend-effectercoordinaterelativetothebasecoordinatewhengiventhegeometricparametersoflinkandthetranslationofjoint.Letmakethingsclearly:

Whatyouaregiven:

thelengthofeachlinkandtheangleofeachjoint

Whatyoucanfind:

thepositionofanypoint（i.e.it’s

coordinate）

3.2Thesolutionofforwardkinematics

Method:

Algebraicsolution

Principal:

Thekinematicmodelofarobotcanbewrittenlikethis,where

denotesthevectorofjointvariable,

denotesthevectoroftaskvariable,

isthedirectkinematicfunctionthatcanbederivedforanyrobotstructure.

Theoriginof

Eachjointisassignedacoordinateframe.UsingtheDenavit-Hartenbergnotation,youneed4parameters（

）todescribehowaframe（

）relatestoapreviousframe（

）

.Fortwoframespositionedinspace,thefirstcanbemovedintocoincidencewiththesecondbyasequenceof4operations:

1.Rotatearoundthe

axisbyanangle

.

2.Translatealongthe

axisbyadistance

.

3.Rotatearoundthenewzaxisbyanangle

.

4.Translatealongthenewzaxisbyadistance

.

（1.1）

（1.2）

Therefore,accordingtothetheoryabovethefinalhomogeneoustransformcorrespondingtothelastlinkofthemanipulator:

（1.3）

3.3Inversekinematic

Definition:

Robotinversekinematicsproblemisthatresolveeachjointvariablesoftherobotbasedongiventhepositionanddirectionoftheend-effecterorofthelink（ItcanshowaspositionmatrixT）.AsforPUMA560Robot,variable

needtoberesolved.

Letmakethingsclearly:

Whatyouaregiven:

Thelengthofeachlinkandthepositionofsomepointontherobot.

Whatyoucanfind:

Theanglesofeachjointneededtoobtainthatposition.

3.4Thesolutionofinversekinematics

Method:

Algebraicsolution

Principal:

Where

istherobotJacobian.JacobiancanbeseenasamappingfromJointvelocityspacetoOperationalvelocityspace.

3.5Thetrajectoryplanningofrobotkinematics

Thetrajectoryplanningofrobotkinematicsmainlystudiesthemovementofrobot.Ourgoalistoletrobotmovesalonggivenpath.Wecandividethetrajectoryofrobotsintotwokinds.Oneispointtopointwhiletheotheristrajectorytracking.Theformerisonlyfocusonspecificlocationpoint.Thelattercaresthewholepath.

Trajectorytrackingisbasedonpointtopoint,buttherouteisnotdetermined.So,trajectorytrackingonlycanensuretherobotsarrivesthedesiredposeintheendposition,butcannotensureinthewholetrajectory.Inordertolettheend-effecterarrivingdesiredpath,wetrytoletthedistancebetweentwopathsassmallaspossiblewhenweplanCartesianspacepath.Inaddition,inordertoeliminateposeandposition’suncertaintybetweentwopathpoints,weusuallydomotivationplanamongeveryjointsundergangcontrol.Inaword,leteachjointhassamerundurationwhenwedotrajectoryplanninginjointspace.

Atsametime,inordertomakethetrajectoryplanningmoresmoothly,weneedtoapplytheinterpolatingmethod.

Method:

polynomialinterpolating[1]

Given:

boundarycondition

（1.3）

（1.4）

Output:

jointspacetrajectory

betweentwopoints

=

（1.5）

Polynomialcoefficientcanbecomputedasfollows:

（1.6）

.KinematicsimulationbasedonMATLAB

Howtouselink

InRoboticsToolbox,function’link’isusedtocreateabar.Therearetwomethods.OneistoadoptstandardD-HparametersandtheotheristoadoptmodifiedD-Hparameters,whichcorrespondtotwocoordinatesystems.WeadoptmodifiedD-Hparametersinourpaper.Thefirst4elementsinFunction‘link’areα,a,θ,d.Thelastelementis0（representRotationaljoint）or1（representtranslationjoint）.Thefinalparameteroflinkis’mod’,whichmeansstandardormodified.Thedefaultisstandard.

Therefore,ifyouwanttobuildyourownrobot,youmayusefunction‘link’.Youcancallitlikethis:

’L1=link（[00pi00],'modified'）;

Thestepofsimulationis:

Step1:

Firstofall,accordingtothedatafromTable1,webuildsimulationprogramoftherobot（showninAppendixrob1.m）.

Step2:

Present3Dfigureoftherobot（showninFig4）.Thisisathree-dimensionalfigurewhentherobotlocatedtheinitialposition（

）.Wecanadjustthepositionofthesliderincontrolpaneltomakethejointrotation（inFig5）,justlikecontrollingrealrobot.

Step3:

PointAlocatedatinitialposition.Itcandedescribedas

.ThetargetpointisPointB.Thejointrotationanglecanbeexpressedas

.Wecanachievethesolutionofforwardkinematicsandobtaintheend-effecterposerelativetothebasecoordinatesystemis（0.737,0.149,0.326）,relativetothethreeaxesofrotationangleisthe（0,0,-1）.Therobot’sthree-dimensionalposein

isshowninFig6.

Step4:

Accordingtothehomogeneoustransformationmatrix,wecanobtaineachjointvariablefromtheinitialpositiontothespecifiedlocation

Step5:

SimulatetrajectoryfrompointAtopointB.Thesimulationtimeis10s.Timeintervalis0.1s.Then,wecanpicturelocationimage,theangularvelocityandangularaccelerationimage（shownasFig8）whichdescribeeachjointtransformsovertimefromPointAtoPointB.Inthispaper,weonlypresentthepictureofjoint3.Byusingthefunction‘T=fkine（r,q）’,weobtain‘T’athree-dimensionalmatrix.Thefirsttwodimensionalmatrixrepresentthecoordinatechangewhilethelastdimensionistime‘t’.

Fig4

Fig5

Fig6

Fig7

Fig8

Theproblemduringthesimulation

Thereasonforselectionofsomeparameter

Theparameteroflink:

Fromkinematicsimulationandprogram,youcanseethatIsetcertainvaluenotarbitrarywhenIcall‘link’.ThatisbecauseIwantthesimulationcanbemoreclosetotherealsituation.So;Iadopttheparameterofpuma560（youcanseeitfromtheprogram）andthereisnodifferencebetweenmyrobotandpuma560radically.

Theparameterof

:

WhenIchoosetheparameterof

Ijustwanttotestsomething.

Forexample,whenyoudenotetheparameterof‘

’likethis‘

’,youwanttousethefunction‘fkine（p560,

）’toobtainthehomogenousfunction‘T’,then,youwanttouse‘ikine（p560,T）’totestwhetherthe‘

’iswhatyouhavesettledbefore.

Theresultisasfollows:

=[0-pi/4-pi/40pi/80];

T=fkine（p560,

）;